If you got a new airport extreme you now have a new wireless network.
Your printer is using the settings for the old router and that is what needs to be changed.
If your printer has a display panel that allows you to change things you can get it connected to the new AE.
Since I don't know what printer you have I can only give general instructions.
On the panel you would look for Settings or Setup and then Network and then Wireless.
Some printers have a Wireless Setup Wizard that when selected will show you the wireless networks
the printer can detect. You would select your wireless network and then enter the wi-fi password.
Once the printer shows as connected your computer should be able to detect it.
If your printer doesn't have a display you'd need to connect it to your Mac via USB and go through
the setup process and specify that you wanted to set the printer up for a wireless connection.